Porous Media Group
MSc project

On the coupling of the Biot model with reactive transport, 2019

Oda Gilhuus Gregusson

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Advisors: Florin Radu and Mats K. Brun

Short description of the project:

In this thesis, we study the iterative solution of coupled flow, mechanics, and transport in deformable porous media. The system is modeled by the quasi-static Biotequations and the advection-diffusion-reaction equation. This model is analyzed numerically by using a variation of the well-known Fixed Stress Splitting method. The spatial discretization employed is piecewise linear Galerkin finite elements for mechanics and transport, and lowest order Raviart-Thomas elements for flow. Additionally, the backward Euler method is employed for the time discretization. Threedifferent alternatives for the stabilization constant introduced by the fixed stress splitting scheme are analyzed, and the optimal choice for this constant is found. The scheme is also analyzed with and without the stabilization terms introduced by linearization of the reaction term in the transport equation, and the result is that this has no impact on the iteration count for the scheme. Moreover, four different reaction terms are studied, and the result is that they are all convergent. We also study the efficiency of the fixed stress splitting scheme by comparing it with two different monolithic schemes. One where only the Biot equations are solved monolithically, and one where the whole system is solved monolithically. The conclusion is that the fixed stress splitting scheme is the most efficient method for solving our system of equations for finer meshes. For coarser meshes, the choice of method is of little consequence. Furthermore, two different domains are studied, the unit square and the L-shaped domain. Performing convergence tests on the system, give results that are consistent with the optimal theoretical convergence rates for both domains.

Link to the thesis at BORA: https://bora.uib.no/bora-xmlui/handle/1956/19968